Parent jealousy is real. I have dealt with it and still do. But really if I let it bug me, then it is just as much my issue as theirs, if that makes sense. When I get comments like "wow, your daughter is really good" or my favorite "I've never seen her fall before" I try to ignore them and just put the ball back in their court. I respond with, "thanks so is your daughter!" or "isn't amazing how all of them just get right back up?" I try really hard to not let it get to me. And sometimes, to be brutally honest, I might just be over sensitive to how others react to my DD having a rough day in the gym or at a meet and their need to comment on it.
Now with that all said. I have two really good friends within our gym. We socialize outside of gymnastics and I know that we are going to be life long friends. But our daughters started gymnastics together, moved to team together and we learned the sport together. Now all 3 of our DD's are at different levels and we are still as tight as ever. So are the girls. Everyone else I am polite to, but I do not go out of my way. I have spent time trying to be welcoming, but over half of the families are gone by the end of their L4 season. I know longer waste my time trying to build actual friendships. Would I let a mom sit by herself at a gym function? No, but I am not going to go out of my way to make small talk day to day either.
I never thought comments like "wow you daughter is really good" or "omg I have never seen her fall" stem from jealousy. Our team parents get along pretty well and we say things like this all the time because we genuinely care and mean it (the really good part). Of course we wish the best for our child but we also hope for the best and care for the other girls. Its out of kindness. Maybe our gym is a little different because it really was more of a laid back fun gym until about two years ago and most of the parents and kids are local so we hang out a lot outside of the gym. Jealousy exists every where and I am sure there is jealousy in and outside of the gym but have never taken similar comments about my DD in any way other than a sincere and hope that when I say things like that, other parents don't take it as jealously but admiration. I think that a lot can be read based on tone and facial expression, so you may be experiencing something different based on those, but now I am going to have to talk with the other parents and see how they interpret comments like that lol.